Derby Science NDR News, Fall, 1998
The Science of Driving, Part 2, or
How "bad" can bad driving be?
by Dr. Todd Wetzel
Where we left off...
I ended the article by pointing out the even if you could come up with a systematic way to determine with precision the absolute fastest driving path, you still have to actually get the driver to go there. So in this article we'll explore some bad driving techniques and see how they compare to each other.
Let's meet our contestants...
So we are going to run 6 different drivers through three different tracks using the computer program developed in the last article. All of the drivers but one has a specific driving flaw. They are:
Sam Perfect driver. He goes out at exactly the correct angle, goes all the way to the cones, and keeps the car on the cones the whole way down.
Dave. Dave is new to this derby thing, and therefore doesn't know much about what's going on. So he just goes straight down middle of the lane.
Drew. Drew goes out at the correct angle, but as soon as he gets to the flags he overcorrects and drifts back to the middle of the lane.
Craig. Craig goes out at exactly the right angle, but he gets a little scared of hitting cones or going off the track, so he only gets within 6" of the cones (or the edge of the lane).
Eric. Eric is having trouble with some sinus medication, so after he gets out to the cones, he swerves back and forth 6". He does ten swerves in about 100' of track before he finally straightens the thing out.
Frankie. Frankie drives real smooth, be he does not go out as aggressively as Sam,
and in fact gets to the cones 20' farther down the hill than Sam.
We're going to race these guys on a mini-Keystone circuit. They will race on a fast track, Similar to York, with 50' of drop; a medium speed track, perhaps Harrisburg, with 30'of drop; and a very slow track, such as Lower Bucks, with 10' of drop. All of the tracks are 1000' long and have a straight crown of 1" drop over 5' of track width. I will use the computer program developed in the last article to find out who wins and by how much in .
Race 1: The fast track
Obviously, Sam is going to win in all of these contrived races because he is the "perfect" driver. But remember, on the fast tracks, you don't need to go out as fast as you do on a slow track. It also turns out on the fast tracks that it is much less important to hit the optimum angle going out. So although Frankie goes out kind of slow, he essentially dead-heats with Sam. Very close behind is Craig, who doesn't drive all the way out to the edge of the track, but instead gets within 6" of the edge. He loses to Sam by only 0.002 overall.
In fourth place is Eric, who you recall tends to swerve a lot. His 10 fairly severe swerves cost him to lose to Sam by only 0.036 overall (or 0.018 per phase). Now on a fast hill like York, 0.036 is a decent win, but like I said, these are very severe swerves. And it's ten swerves, not one. I personally expected this to be more of a problem, and it might be. If you recall from the last article, the computer program models the exchange of energy as one drives down the hill. So most of the 0.036 is actually due to the fact that Eric takes a longer path down the hill by swerving back and forth. Additionally, he lost a tiny amount of time because as he swerved he was also going "up" and "down" the crown of the hill, but analysis shows that this loss is very small compared to the fact that he is taking a longer path down the hill. What is not included in the model is the increase in rolling resistance drag due to "scrubbing" the tires or loading the bearings as you steer. Truthfully, to my knowledge there is not enough data available to develop a believable model for such wheel losses on a derby car. And even if there was such a model, chances are the losses are quite low, because: a) a properly aligned derby car has "perfect" steering (all 4 wheels are tangent to circles with the same center) due to steering with a swinging solid axle, and b) even the quickest turn in a derby car under normal driving situations leads to a fairly large turning radius and therefore low centrifugal force turns. All of these facts mean the wheel losses are probably very small, but I can't prove that quantitatively. So that's why I ignore wheel losses. But in Eric's case, it is possible that properly modeling wheel losses would cause him to lose by even more.
Right behind Eric in fifth place is Drew, who you may recall overcorrected and drifted back to the middle of the lane. Drew loses to Sam by 0.052 overall. And in last place, where he belongs, is poor Dave, who just went straight down the center of the lane. He loses to Sam by 0.064 overall. It is interesting to note that even though Drew and Dave spent most of the time in the center of the lanes, Drew won because he at least went out at the top of the hill. So if your driver is overcorrecting but at least going out, he is doing better than if he were just going straight down the hill. Also, Eric's ten swerves were almost enough to negate any gains he got from going out.
Race 2: The medium track
Race 3: The slow track ("Lower Bucks")
Now things are getting interesting. Very slow tracks can often shuffle up points standings. The Keystone circuit holds races on a slow track in Lower Bucks county (Philadelphia), and used to race on a very flat track in State College in the '80's. In fact, at one State College race I raced at, way way way back in the old days (mid 80's), the first heat did not even make it to the finish line, so the finish line had to be moved up the track a little. To some people, pure derby racing means steep straight hills. But very slow hills like these are great tests of driving ability, and driver attention span!
As I have seen in many real races, our finishing order gets surprisingly mixed up a little on this simulated track. Sam of course wins, but Craig is in second by 0.096 overall. For those of you who have never raced on such a slow track, keep in mind that since the cars are going so much slower at the finish line, the overall times are considerably larger. For example, Craig lost each of these phases by a little more than an inch! And now in third is Eric, finishing only 0.142 behind Sam. I would not have thought that you can get away with such serves on a slow hill.
Very surprisingly, Frankie ends in fourth this time, 0.206 behind Sam. Remember, on the slowest tracks you need to attack the crown aggressively and get out very fast. Frankie takes his time getting out, and while it doesn't hurt him much on other tracks, it kills him on this slow track. Drew's over-correction on this track really hurts, as he loses to Sam by 1.198 seconds overall. Yes, over a second! So when you race on these slow hills, whatever you do, GET OUT AND STAY OUT. And of course, Dave completes a pitiful campaign, finishing in last again, 1.414 seconds behind Sam.
Here is a summary of the results. In the table is how much each of the drivers would lose to Sam overall (two phases):
North/South Showdown: "Virginia
But back in the day when the editor and I were racing Keystone, the last fall Keystone rally was at a track in Virginia Beach. This was a great way to end the season, traveling to the "warmer" south (I've raced in some freezing weather in Virginia), and getting to race some of the fast cars from the south, especially North Carolina at the time. I understand there is an organization racing out of Virginia Beach again. It's a good thing, because that was one of the most interesting tracks I'd ever raced on. It is built on top of an old landfill called "Mount Trashmore", and over the years, this landfill has settled considerably. So the track at Virginia Beach has an undulating surface, and in particular the crown switches from normal (going out) at the top to coming in at the bottom (unless it has changed again in the last 12 years since I last raced there!). So typically drivers would go out at the top and come back in at the bottom, following the crown. It was quite exciting to see two cars muscle close to each other in the center of the track, both trying to squeeze out more track on the centerline!
So our racers, especially the "perfect driver' Sam, head to a simulated version of the Virginia Beach track. We will model it the same as York, but now we will make the crown gradually shift from "out" at the top to "in" at the bottom. And now a new driver shows up. Maggie is her name, and she drives as good as Sam EXCEPT she comes in at the bottom of the hill. She decides to wait until the bottom of the hill to come back in, since on our modeled track this is where the inward crown is steepest. So on the track I am modeling, Sam and Maggie both go out to the edge of their lanes in the first 75', then they both stay outside, until 75' from the finish line, at which point Maggie starts coming back in. Who is going to win?
Surprisingly, Sam still wins, this time by 0.006 overall. This puts Maggie potentially in 4th place behind Frankie and Craig. Remember, Maggie is driving with the crown and thus going downhill a little more than Sam, but she is doing it at the expense of a longer path down the hill. In this example, Maggie's path is 2" longer than Sam's. Since she is gaining this crown only at the bottom of the hill, she can't make use of the extra speed for very long, and what she gains in speed is less than what she loses in path length.
So Maggie is in the losers bracket, working her way back up to race Sam for first place. Now the reason her path length is longer is mainly because she is waiting until the end to come in. What if she comes in earlier? It turns out the earlier she starts to come back in, the shorter her total path length is. So, for example, if she starts coming in 750' from the finish line instead of 75' from the finish line, her path length is only 0.2" longer than Sam's, and maybe then the crown will help her. So in the last heat of the day, Maggie tries this gentle drift as opposed to darting in, and guess what, she WINS by 0.006 overall. So by drifting very slowly, she was able to take advantage of the crown without taking longer to get there.
Happy (and safe) driving!
So hopefully these examples will help especially for younger drivers who are still honing their skills. Focus first on getting your driver to go out aggressively, and then work hard on getting them to keep the car out on the edge of the lane. There are a lot of drivers who progress to this stage well, but if you watch them coming down the hill, they are working very hard to keep the car on the edge of the lane and keep it straight, making dozens of little corrections back and forth. So to me the distinction between a good driver and a great driver is when a driver can get the car to the edge of the lane and keep it there, without having to correct the car over and over again. Of course a lot of this is a function of the alignment of the car, but it is also a function of the experience and maturity of the driver. When I get to this stage with a driver, I try to convince them to ease their grip on the wheel (at least on smoother tracks) and let the car roll down the hill free with as few corrections as possible. I ask them to count how many times they actually move the steering wheel after they've gotten to the edge of the lane (hoping, of course, that counting will not distract them from the driving tasks at hand!), and we work on trying to reduce that number from dozens to a couple. And especially from Maggie's example, perhaps letting the car roll where it wants to, even if it is coming off the cones, might be the best, so long as the car is drifting very slowly. Part of the reason Drew gets hurt bad in this simulation is he comes off the cones fairly quickly (thus increasing his path length) and he does so at the top of the hill, where his loss of speed is carried down the rest of the hill and just builds up more and more lost time. If Drew were to drift in very gradually over a major length of the hill, he would probably only barely lose, and be in there with the likes of Craig and Frankie. Good luck!
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